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Sketch qualitatively accurate graphs of G vs. P for the three phases of H20 (ice, water, and steam) at 0°C. Put all three graphs on the same set of axes, and label the point corresponding to atmospheric pressure. How would |the graphs differ at slightly higher temperatures?

Short Answer

Expert verified

As the temperature rises above 0°C, the ice curve shifts to the left of the steam curve.

Step by step solution

01

Given information

From the thermodynamic potential from the Gibbs free energy at constant temperature, we have

∂G∂PT,N=V

Where,

P is pressure

V is volume

We will use the above equation to draw the graph with slope ∂G∂P.

02

Explanation 

The graph below represents the three phases of H2O at 0 degree temperature.

The ice graph is steeper than the water graph in this instance. The slope of steam is steeper than the graphs of ice and water. The compressibility of steam is greater than that of ice and water. As a result, it has a downward curvature, as indicated in the diagram above.

03

Explanation 

Gibbs free energy's temperature dependency is given as

∂G∂TP.N=-S

Where,

G id Gibbs free energy

T is temperature

S is entropy of system

Using the preceding equation, the Gibbs free energy of H2O will decreases during each phase. The steam phase of H2O has a higher entropy than the water and ice phases. As a result, Gibbs free energy decreases more in the steam phase and less in the ice phase.

As the temperature rises above 0°C, the ice curve shifts to the left of the steam curve, as seen in the diagram.

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Most popular questions from this chapter

Plot the Van der Waals isotherm for T/Tc = 0.95, working in terms of reduced variables. Perform the Maxwell construction (either graphically or numerically) to obtain the vapor pressure. Then plot the Gibbs free energy (in units of NkTc) as a function of pressure for this same temperature and check that this graph predicts the same value for the vapor pressure.

Sketch qualitatively accurate graphs of Gvs.Tfor the three phases ofH2O(ice, water, and steam) at atmospheric pressure. Put all three graphs on the same set of axes, and label the temperatures0°Cand 100°C. How would the graphs differ at a pressure of0.001bar?

Prove that the entropy of mixing of an ideal mixture has an infinite slope, when plotted vs. x, at x = 0 and x= 1.

Calculate the Helmholtz free energy of a van der Waals fluid, up to an undetermined function of temperature as in equation5.56. Using reduced variables, carefully plot the Helmholtz free energy (in units of NkTc) as a function of volume for T/Tc=0.8Identify the two points on the graph corresponding to the liquid and gas at the vapor pressure. (If you haven't worked the preceding problem, just read the appropriate values off Figure5.23.) Then prove that the Helmholtz free energy of a combination of these two states (part liquid, part gas) can be represented by a straight line connecting these two points on the graph. Explain why the combination is more stable, at a given volume, than the homogeneous state represented by the original curve, and describe how you could have determined the two transition volumes directly from the graph of F.

Compare expression 5.68 for the Gibbs free energy of a dilute solution to expression 5.61 for the Gibbs free energy of an ideal mixture. Under what circumstances should these two expressions agree? Show that they do agree under these circumstances, and identify the function f(T, P) in this case.

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